# Tree based functional expansions for Feynman--Kac particle models

Abstract : We design exact polynomial expansions of a class of Feynman--Kac particle distributions. These expansions are finite and are parametrized by coalescent trees and other related combinatorial quantities. The accuracy of the expansions at any order is related naturally to the number of coalescences of the trees. Our results include an extension of the Wick product formula to interacting particle systems. They also provide refined nonasymptotic propagation of chaos-type properties, as well as sharp $\mathbb{L}_p$-mean error bounds, and laws of large numbers for $U$-statistics.
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The Annals of Applied Probability : an official journal of the institute of mathematical statistics, The Institute of Mathematical Statistics, 2009, pp.778-825. <10.1214/08-AAP565>
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https://hal.archives-ouvertes.fr/hal-00086532
Contributeur : Patras Frédéric <>
Soumis le : mercredi 19 juillet 2006 - 09:24:23
Dernière modification le : mercredi 4 mai 2016 - 13:30:50
Document(s) archivé(s) le : lundi 5 avril 2010 - 22:10:02

### Citation

Pierre Del Moral, Frédéric Patras, Sylvain Rubenthaler. Tree based functional expansions for Feynman--Kac particle models. The Annals of Applied Probability : an official journal of the institute of mathematical statistics, The Institute of Mathematical Statistics, 2009, pp.778-825. <10.1214/08-AAP565>. <hal-00086532>

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